A lens can produce an image (a reproduction of the spatial variations of intensity) of an object at some distance s_i where 1/f = 1/si + 1/so. However, a lens also produces a spatial Fourier transform of the intensity variations in the transverse plane at the focal plane of the lens. Just as you can filter a time varying signal (say a voltage or current) by inserting low, high, or band pass filters, so can you filter a spatially varying signal (the image from a lens) by inserting blocks or phase plates at the fourier transform plane.

In this lab you will explore the results of "spatial filtering" in an image forming system.

You will also explore the diffraction of light from objects. You will investigate, for example, the Poisson spot which is one of the most surprising and famous examples of how light doesn't just travel in straight lines. By understanding the behavior of a diffraction pattern with wavelength you can determine the size and shape of a microscopic diffracting object by measuring the characteristics of the angular diffraction pattern.

When light is divided by a beam splitter, the wave which reflects from the surface and the one which passes through the surface are copies of each other. These two waves, if brought back together, can interfere constructively and destructively to produce light and dark "fringes". The position of these fringes depends on the wavelength and path length that the two beams follow. When white light is used (many colors and therefore many wavelengths) the fringe patterns from each color have a different position and spacing - the result is that you only see fringes when the path length difference between the two paths is exactly *zero* (or close to it). In this case, although the transverse spacing of the fringes is slightly different, at least the position of the fringes is the same and therefore you will see the central maxima (or minima) and a number of fringes as you move away from the center.

You will align the interferometer and find the condition for zero path length difference. (this means making the path lengths the same by translating one of the mirrors).

The path length difference range over which you can still see fringes is called the "coherence length" and is inversely related to the bandwidth of colors in the light. For white light, the bandwidth is large and the coherence length is small (close to zero), but for monochromatic laser light the bandwidth is small and the coherence length is large - in which case you see fringes even for very different path lengths.

In class we saw that a beam made of two distinct colors decomposes into a carrier plus a modulation - likewise for the interference pattern you will see an envelope function on the fringe visibility which will allow you to measure the frequency difference between two emission lines from a sodium lamp.